I think that's a no-go. I believe fishing rods and similar are actually banned as carry-on on all flight to and from the EU, typical knee jerk reaction by legislators desperate to appear to be doing SOMETHING. Flying BA and then perhaps LHR as well reduces your chances further, they both seem particularly eager to apply the strictest possible enforcement on even the most pointless of rules.
ps! Be real careful around Nassau, you might see arriving American carriers, which might very well be filled with yankees holding their precious fishing rods inside the cabin. How these planes make there without being hijacked is something you can ponder while you stand in line waiting to file a missing luggage claim...
